11institutetext: Università degli Studi di Firenze - MICC,
11email<EMAIL_ADDRESS>
Firenze, Italy 22institutetext: Università di Pisa
Pisa, Italy

# Exploiting CLIP-based Multi-modal Approach for Artwork Classification and
Retrieval

Alberto Baldrati 1122 Marco Bertini 11 Tiberio Uricchio 11
Alberto Del Bimbo 11

###### Abstract

Given the recent advantages in multimodal image pretraining where visual
models trained with semantically dense textual supervision tend to have better
generalization capabilities than those trained using categorical attributes or
through unsupervised techniques, in this work we investigate how recent CLIP
model can be applied in several tasks in artwork domain. We perform exhaustive
experiments on the NoisyArt dataset which is a collection of artwork images
collected from public resources on the web. On such dataset CLIP achieve
impressive results on (zero-shot) classification and promising results in both
artwork-to-artwork and description-to-artwork domain.

###### keywords:

image retrieval, zero-shot classification, artwork, CLIP

##  1 Introduction

Image Classification and Content-Based Image Retrieval (CBIR) are fundamental
tasks for many domains, and have been thoroughly studied by the multimedia and
computer vision communities. In cultural heritage domain, these tasks allow to
simplify the management of large collections of images, allowing to annotate,
search and explore them more easily and with lower costs.

In the latest years neural networks have proved to outperform engineered
features in both tasks. These networks are typically used in an unimodal
fashion, i.e. only one media is used to train and use a network. This may
limit the types of application that can be developed and may also reduce the
performance of the networks. Several recent works are showing how using multi-
modal approaches may improve the performance in several tasks related to
visual information. In [17] it has been shown that CLIP, a model trained using
an image-caption objective alignment on a giant dataset made of 400 million
(image, text) pairs, obtain impressive results on several downstream tasks.
The authors pointed out that, using only textual supervision, CLIP model
learns to perform a wide set of tasks during pre-training including OCR, geo-
localization, action recognition and many others. This task learning can be
leveraged via natural language prompting to enable zero-shot transfer to many
existing dataset.

In this work we try to exploit the zero-shot capabilities of CLIP in the
artworks domain, in particular we focus on the NoisyArt [2] dataset which is
originally designed to support research on webly-supervised recognition of
artworks and Zero-Shot Learning (ZSL). Webly-supervised learning is
interesting since it allows to greatly reduce annotation costs required to
train deep neural networks, thus allowing cultural institutions to train and
develop deep learning methods while keeping their budgets for the curation of
their collections rather than the curation of training datasets. In Zero-Shot
Learning approaches visual categories are acquired without any training
samples, exploiting the alignment of semantic and visual information learned
on some training dataset. ZSL in artwork recognition is a problem of instance
recognition, unlike the other common ZSL problems that address class
recognition. Zero-shot recognition is particularly appealing for cultural
heritage and artwork recognition, although it is an extremely challenging
problem, since it can be reasonably expected that museums have a set of
curated description paired with artworks in their collections.

To get a better idea of how CLIP behaves in the artworks domain we started
with a classification task using a shallow classifier and CLIP as the
backbone. Subsequently, thanks to the descriptions of the artworks in the
dataset, we performed experiments in the field of zero-shot classification
where CLIP was able to demonstrate its abilities in this task. Finally, we
performed experiments on the tasks of artwork-to-artwork and description-to-
artwork retrieval obtaining very promising results and superior performance to
a ResNet-50 pre-trained on ImageNet [19]

##  2 Related Works

Regarding CBIR, after the introduction of the successful Bag-of-Visual-Words
model in [23] that use engineered visual features such as SIFT points, many
works have improved the performance addressing different aspects such as
approximating local descriptors [8], learning improved codebooks [14],
improving local features aggregation [15, 9, 4]. In the last years, following
the success obtained using Convolutional Neural Networks (CNN) to address the
problem of image classification [12], CNN-based features have started to be
used also for image retrieval tasks. A complete survey that compares SIFT-
based and CNN-based methods for instance-based image retrieval is presented in
[28]. Commonly used backbone networks are VGG [22] and ResNet [7], typically
pretrained on ImageNet and then fine tuned for a specific domain. CNN features
have been pooled using techniques like Regional maximum activation of
convolutions (R-MAC) [25]. R-MAC considers a set of fixed squared regions at
different scales, collecting the maximum response in each channel and then
sum-pooling them to create the final R-MAC descriptor. More recent works
follow an end-to-end approach: in [1] has been proposed a layer called
NetVLAD, pluggable in any CNN architecture and trainable through back-
propagation, that allows to train end-to-end a network using an aggregation of
VGG16 convolutional activations. Multi-scale pooling of CNN features followed
by NetVLAD has been proposed in [26], obtaining state-of-the-art results using
VGG16. In [16] a trainable pooling layer called Generalized-Mean (GeM) has
been proposed, along with learning whitening, for short representations. In
this work a two stream Siamese network is trained using contrastive loss. The
authors use up to 5 image scales to extract features.

##  3 Dataset

NoisyArt [2] is a collection of artwork images collected using articulated
queries to metadata repositories and image search engines on the web.
According to the creators of the dataset, the goal of NoisyArt is to support
research on webly-supervised artwork recognition for cultural heritage
applications.

In Table 1 the characteristics of the NoisyArt dataset are summarized

|  | (webly images) | (verified images)
---|---|---|---
| classes | training | validation | test
| 2,920 | 65,759 | 17,368 | 0
| 200 | 4,715 | 1,253 | 1,355
totals | 3,120 | 70,474 | 18,621 | 1,355
Table 1: Characteristics of the NoisyArt dataset

NoisyArt is a complex dataset which can be used on a wide variety of automated
recognition problems. The dataset is particularly well suited to webly
supervised instance recognition as a weakly-supervised extension of fully-
supervised learning. In the dataset, for testing purposes, a subset of classes
with manually verified test images is provided (i.e. with no label noise).

The NoisyArt dataset is collected from numerous public resources available on
the web. These resources are DBpedia (where also the metadata are retrieved),
Google Images and Flickr. Figure 1 shows some examples of artworks with their
respective sources.

Figure 1: Sample classes and training images from the NoisyArt dataset. For
each artwork/artist pair we show the seed image obtained from DBpedia, the
first two Google Image search results, and first two Flickr search. Image
taken from [2]

From these sources the authors collected 89,095 images divided into 3,120
classes. Each class contains a minimum of 20 images and a maximum of 33. To
make sure to have a non-noisy and more reliable test set the authors decided
to create a supervised test set using a small subset of the original classes:
200 classes containing more than 1,300 images taken from the web or from
personal photos. This test set is not balanced: for some classes we have few
images, and some others have up to 12. The different method of collecting
training and test sets also raises the issue of a strong domain shift between
these images and those in the training set. Finally, each artwork has a
description and metadata retrieved from DBpedia, from which a single textual
document was created for each class. These descriptions are included in the
dataset to support research on zero-shot learning and other multi-modal
approaches to learning over weakly supervised data.

###  3.1 GradCAM visualization

In order to have a better idea of the portions of the image that CLIP
considers most important when it associates a text with an image, before
moving on to the quantitative experiments, we carried out some qualitative
tests using the well-know visualization technique gradCAM [21]. The technique
we used is a generalization of gradCAM, where, instead of computing gradients
with respect to an output class, gradients are computed with respect to
textual features computed with CLIP’s text encoder from the description. This
approach makes each heat-map calculated by gradCAM dependent on the individual
description, showing us the portions of the image that CLIP most closely
associates with it. As a common practice the saliency layer used is the last
convolutional layer of CLIP’s visual encoder.

Figure 2 shows four examples of gradCAM visualization. We can see how, using
the descriptions in the dataset, CLIP places attention to the most significant
portions of the image. This fact made us confident that CLIP would work very
well in the domain of artwork.

Figure 2: Examples of gradCAM visualization on NoisyArt computing the
gradients with respect to the description CLIP text features

##  4 Experiments

###  4.1 Webly-supervised Classification

To test the performance of CLIP in the art domain, following the experimental
setup followed by the authors of the dataset, we performed a webly-supervised
classification on the 200 classes that are also available in the test set.

####  4.1.1 Experimental Setup

Given an input image $\mathbf{x}$, we extract a feature vector using only the
CLIP image encoder and then we pass it through a shallow classifier,
consisting of a single hidden layer and an output layer that estimates class
probabilities $p(c\mid\mathbf{x})$. The hidden layer is followed by an
$L^{2}$-normalization layer which, as noted in [3], helps to create similar
representations for image with different visual characteristics because the
magnitude of features is ignored by the final classification layer. Such
normalization is therefore useful to alleviate the effects of the domain shift
between training and test set.

The structure of the shallow classifier is basically the same of [2, 10]. This
choice was made intentionally to analyze the effects of using the CLIP image
encoder instead of a convolutional backbone trained on ImageNet. For
mitigating and identifying label noise during training in [2] several
techniques like Labelflip noise, entropy scaling for Outlier Mitigation and
Gradual Bootstrapping are used. In our experiments however, following [3], we
only use the $L^{2}$-normalization layer after the hidden layer.

We trained such shallow classifier for 300 epochs with a batch size of 64, the
learning rate used was $1e-4$. We used the CLIP model which has as
convolutional backbone a slightly modified version of the ResNet-50. The
hidden layer has an input dimension of 1024 (CLIP output dimension) and output
dimension of 4096.

####  4.1.2 Experimental Results

| test | validation
---|---|---
Model | acc | mAP | acc | mAP
RN50 BL [2] | 64.80 | 51.69 | 76.14 | 63.08
RN50 BS [2] | 68.27 | 57.44 | 75.98 | 62.83
RN50 $\mathbf{\alpha=0.4}$ [3] | 74.89 | 62.86 | 77.14 | 63.71
CLIP RN50 | 86.63 | 77.88 | 83.56 | 72.23
Table 2: Recognition accuracy (acc) and mean Average Precision (mAP) on
NoisyArt dataset

Table 2 summarizes the experimental results we obtained in this classification
setting. In the table BL refers to the baseline network [2] without any sort
of label mitigating approach, BS refers to the noisy mitigating approach of
[2] and RN50 $\alpha=0.4$ refers to the normalization approach of [3] where
the $L^{2}$-normalization is scaled by $\alpha$.

From the table it is immediately evident that with the use of CLIP as a
backbone it is possible to obtain very significant improvements both on the
test and the validation set. It is very interesting to see that [2, 3] have
better results on validation than on the test set. In our case, however, the
situation is reversed by having comparable and slightly better results on the
test set. This demonstrates how CLIP is quite robust to domain shift being it
able to extract the semantic of an image regardless of its raw content.

###  4.2 Zero-shot Classification

The availability of descriptions associated with artwork made it possible to
perform experiments in the area of zero-shot classification by exploiting
CLIP’s ability to assign a similarity score between text and images.

####  4.2.1 Experimental Results

Model | acc | mAP
---|---|---
DEVISE RN50 [6] | 24.79 | 31.90
EsZSL RN50 [18] | 25.63 | 29.89
COS+NLL+L2 RN50 [3] | 34.93 | 45.53
CLIP RN50 | 60.27 | 69.23
Table 3: Zero-shot recognition accuracy (acc) and mean Average Precision (mAP)
on NoisyArt dataset

Table 3 shows the immense potential in the zero-shot classification domain of
CLIP. As a matter of fact, comparing the results with those found in the
literature, we notice that by using CLIP, improvements of over 20% can be
achieved. It is also worth noting that the results we have compared ours with
have been achieved through a training process that uses a three-fold cross
validation where the 200 verified classes are divided into 150 for
training/validation and 50 for zero-shot test classes. On our side we used
CLIP out-of-the-box without any training on NoisyArt dataset.

In order to make a complete argument, it is also necessary to mention that
since the data on which CLIP was actually trained is not public, we do not
know if any images from this dataset were used in its training process. If so
we would have some sort of leak of information that would make the comparison
less fair.

###  4.3 Image Retrieval

Seeing the excellent behavior of CLIP in the (zero-shot) classification of
artwork, we decided to perform some experiments in image retrieval.

In all the experiments that we are going to present, the images contained in
the validation set (1253 images belonging to the 200 verified classes) were
used as queries, while those of the test set (1379 images of the same 200
classes) were used as index images.

####  4.3.1 Experimental Setup

We have conducted numerous experiments to make sure that we have a complete
idea of how CLIP performs in this task on the NoisyArt dataset. As in
classification experiments the CLIP model which has as visual backbone a
modified version of the ResNet-50 is used.

The most natural way to use CLIP in retrieval is obviously to use the output
of the visual encoder as global descriptor comparing only the visual features,
that is exactly what we did initially as a first experiment.

To take advantage of the CLIP textual encoder and of its goodness in zero-shot
classification, we then reinterpreted the image-to-image retrieval task as
zero-shot classification followed by text-to-image retrieval. This
reinterpretation was made possible by the description and the metadata
associated to each class. Thus given a query, zero-shot classification of that
image was performed as first phase, by exploiting CLIP’s ability to link
images and texts. We therefore used CLIP to assign a similarity score to each
possible (query image, artwork description) pair using the description with
the highest score in the second phase.

The second phase consists in comparing the description chosen at the end of
the first one with all the images in the dataset, assigning a similarity score
to each possible (query description, index image). For a complete comparison
in the results we have also reported an experiment where the first part of
classification is bypassed and the correct monument is always used in the
text-to-image retrieval phase.

Another setup we experimented with consists in adding to the zero-shot
classification followed by text-to-image retrieval experiment as a re-ranking
phase where the first 100 retrieved images are re-ordered using the similarity
of the visual features.

Finally, the CLIP network was fine-tuned for adapting to this task. The fine-
tuning process was done by inserting a shallow classifier composed of two
linear layers at the output of the visual encoder. The learning rate was set
to $1e-7$ for the CLIP encoder (keeping the normalization layers frozen) and
$1e-4$ for the shallow classifier. For ease of use, a classification loss
(categorical cross-entropy) was used during this fine-tuning process. We fine-
tuned the model for 30 epochs using the 2,920 classes not included in the test
set.

####  4.3.2 Experimental Results

Before commenting on the results obtained we summarize the experimental
setups:

  * •

RN50 image features: We compare the image features extracted with a ResNet-50
pretrained on ImageNet

  * •

CLIP image features: We compare the image features extracted with the CLIP
image encoder

  * •

CLIP class + text-to-image: We perform a zero-shot classification of the query
followed by a text-to-image retrieval using CLIP text and visual encoder

  * •

CLIP class + text-to-image + visual re-ranking: We perform a visual re-ranking
of the first 100 retrieved results after CLIP zero-shot classification and
text-to-image retrieval

  * •

Oracle + CLIP text-to-image: We perform only the text-to-image retrieval using
the ground-truth class for the description

  * •

CLIP fine-tuned image features: We compare the image features extracted with
the CLIP image encoder after fine-tuning

Experimental Setup | mAP
---|---
RN50 image features | 36.32
CLIP image features | 46.40
CLIP class + text-to-image | 40.54
CLIP class + text-to-image + visual re-ranking | 47.41
Oracle + CLIP text-to-image | 54.21
CLIP fine-tuned image features | 69.60
Table 4: Retrieval results on NoisyArt dataset using as queries the validation
set and as index images the test set.

Table 4 summarizes the results of the experiments performed in the image
retrieval setting previously described. It can be seen that CLIP visual
features perform better than features extracted with a ResNet-50 pre-trained
on ImageNet. It is interesting to note that the re-ranking process makes the
retrieval process performed by a zero-shot classification followed by a text-
to-image retrieval operation more performing than the approach which uses only
the visual features pre fine-tuning. This fact is obviously made possible by
CLIP’s good results in zero-shot classification illustrated in previous
section. It is also worth mentioning that using the ground-truth class and
performing the text-to-image retrieval operation yields surprisingly good
results: this confirms the goodness of CLIP in the text-to-image retrieval
task. These results are even greater, by a significant margin, than those
obtained using only visual features pre fine-tuning. This is probably due to
the domain shift between validation and test set the visual features are more
subject to. Finally, we can see that CLIP fine-tuning was very successful,
bringing a very significant performance boost and achieving better results
than all other approaches.

##  5 Conclusions

In this paper we propose to use the zero-shot capabilities of CLIP in the
artworks domain, showing how this approach can greatly improve over competing
state-of-the-art approaches in the challenging NoisyArt dataset. Experiments
show that in addition to zero-shot classification, the proposed approach can
be used for content-based image retrieval, again outperforming by a large
margin other competing approaches. A benefit of using the proposed method is
that it can be trained using very small datasets, thanks to the extensive
pretraining of CLIP, and thus the method can be deployed also to be used on
relatively small collections like those of small and medium-sized museums.

##### Acknowledgments

This work was partially supported by the European Commission under European
Horizon 2020 Programme, grant number 101004545 - ReInHerit.

## References

  * Arandjelovic et al. [2016] R. Arandjelovic, P. Gronat, A. Torii, T. Pajdla, and J. Sivic.  NetVLAD: CNN architecture for weakly supervised place recognition.  In _Proc. of CVPR_ , 2016.
  * Del Chiaro et al. [2019] R. Del Chiaro, A. D. Bagdanov, and A. Del Bimbo.  Noisyart: A dataset for webly-supervised artwork recognition.  In _VISIGRAPP (4: VISAPP)_ , pages 467–475, 2019.
  * Del Chiaro et al. [2019] R. Del Chiaro, A. D. Bagdanov, and A. Del Bimbo.  Webly-supervised zero-shot learning for artwork instance recognition.  _Pattern Recognition Letters_ , 128:420–426, 2019.  ISSN 0167-8655.  https://doi.org/10.1016/j.patrec.2019.09.027.  URL https://www.sciencedirect.com/science/article/pii/S0167865519302739.
  * Delhumeau et al. [2013] J. Delhumeau, P.-H. Gosselin, H. Jégou, and P. Pérez.  Revisiting the VLAD image representation.  In _Proc. of ACM MM_ , 2013.
  * Desai and Johnson [2021] K. Desai and J. Johnson.  VirTex: Learning Visual Representations from Textual Annotations.  In _CVPR_ , 2021.
  * Frome et al. [2013] A. Frome, G. S. Corrado, J. Shlens, S. Bengio, J. Dean, M. A. Ranzato, and T. Mikolov.  Devise: A deep visual-semantic embedding model.  In C. J. C. Burges, L. Bottou, M. Welling, Z. Ghahramani, and K. Q. Weinberger, editors, _Advances in Neural Information Processing Systems_ , volume 26. Curran Associates, Inc., 2013.  URL https://proceedings.neurips.cc/paper/2013/file/7cce53cf90577442771720a370c3c723-Paper.pdf.
  * He et al. [2016] K. He, X. Zhang, S. Ren, and J. Sun.  Deep residual learning for image recognition.  In _Proc. of CVPR_ , pages 770–778, 2016.  10.1109/CVPR.2016.90.
  * Jégou et al. [2010] H. Jégou, M. Douze, and C. Schmid.  Improving bag-of-features for large scale image search.  _International Journal of Computer Vision_ , 87(3):316–336, 2010.  10.1007/s11263-009-0285-2.  URL https://doi.org/10.1007/s11263-009-0285-2.
  * Jégou et al. [2012] H. Jégou, F. Perronnin, M. Douze, J. Sánchez, P. Pérez, and C. Schmid.  Aggregating local image descriptors into compact codes.  _IEEE Transactions on Pattern Analysis and Machine Intelligence_ , 34(9):1704–1716, Sep. 2012.  ISSN 1939-3539.  10.1109/TPAMI.2011.235.
  * Kalantidis et al. [2016] Y. Kalantidis, C. Mellina, and S. Osindero.  Cross-dimensional weighting for aggregated deep convolutional features, 2016.
  * Kolesnikov et al. [2020] A. Kolesnikov, L. Beyer, X. Zhai, J. Puigcerver, J. Yung, S. Gelly, and N. Houlsby.  Big transfer (bit): General visual representation learning, 2020.
  * Krizhevsky et al. [2012] A. Krizhevsky, I. Sutskever, and G. E. Hinton.  Imagenet classification with deep convolutional neural networks.  In _Proc. of NIPS_ , 2012.
  * Mahajan et al. [2018] D. Mahajan, R. Girshick, V. Ramanathan, K. He, M. Paluri, Y. Li, A. Bharambe, and L. van der Maaten.  Exploring the limits of weakly supervised pretraining, 2018.
  * Mikulik et al. [2013] A. Mikulik, M. Perdoch, O. Chum, and J. Matas.  Learning vocabularies over a fine quantization.  _International Journal of Computer Vision_ , 103(1):163–175, 2013.
  * Perronnin et al. [2010] F. Perronnin, J. Sánchez, and T. Mensink.  Improving the Fisher kernel for large-scale image classification.  In _Proc. of ECCV_ , 2010.
  * Radenović et al. [2018] F. Radenović, G. Tolias, and O. Chum.  Fine-tuning CNN image retrieval with no human annotation.  _IEEE Transactions on Pattern Analysis and Machine Intelligence_ , 41(7):1655–1668, 2018.
  * Radford et al. [2021] A. Radford, J. W. Kim, C. Hallacy, A. Ramesh, G. Goh, S. Agarwal, G. Sastry, A. Askell, P. Mishkin, J. Clark, G. Krueger, and I. Sutskever.  Learning transferable visual models from natural language supervision, 2021.
  * Romera-Paredes and Torr [2015] B. Romera-Paredes and P. Torr.  An embarrassingly simple approach to zero-shot learning.  In F. Bach and D. Blei, editors, _Proceedings of the 32nd International Conference on Machine Learning_ , volume 37 of _Proceedings of Machine Learning Research_ , pages 2152–2161, Lille, France, 07–09 Jul 2015\. PMLR.  URL https://proceedings.mlr.press/v37/romera-paredes15.html.
  * Russakovsky et al. [2015] O. Russakovsky, J. Deng, H. Su, J. Krause, S. Satheesh, S. Ma, Z. Huang, A. Karpathy, A. Khosla, M. Bernstein, A. C. Berg, and L. Fei-Fei.  Imagenet large scale visual recognition challenge, 2015.
  * Sariyildiz et al. [2020] M. B. Sariyildiz, J. Perez, and D. Larlus.  Learning visual representations with caption annotations, 2020.
  * Selvaraju et al. [2019] R. R. Selvaraju, M. Cogswell, A. Das, R. Vedantam, D. Parikh, and D. Batra.  Grad-cam: Visual explanations from deep networks via gradient-based localization.  _International Journal of Computer Vision_ , 128(2):336–359, Oct 2019.  ISSN 1573-1405.  10.1007/s11263-019-01228-7.  URL http://dx.doi.org/10.1007/s11263-019-01228-7.
  * Simonyan and Zisserman [2014] K. Simonyan and A. Zisserman.  Very deep convolutional networks for large-scale image recognition.  _arXiv preprint arXiv:1409.1556_ , 2014.
  * Sivic and Zisserman [2003] J. Sivic and A. Zisserman.  Video google: a text retrieval approach to object matching in videos.  In _Proc. of ICCV_ , Oct 2003.  10.1109/ICCV.2003.1238663.
  * Socher et al. [2013] R. Socher, M. Ganjoo, C. D. Manning, and A. Ng.  Zero-shot learning through cross-modal transfer.  _Advances in neural information processing systems_ , 26, 2013.
  * Tolias et al. [2016] G. Tolias, R. Sicre, and H. Jégou.  Particular object retrieval with integral max-pooling of CNN activations.  In _Proc. of ICLR_ , 2016.
  * Vaccaro et al. [2020] F. Vaccaro, M. Bertini, T. Uricchio, and A. Del Bimbo.  Image retrieval using multi-scale CNN features pooling, 2020.
  * Zhang et al. [2020] Y. Zhang, H. Jiang, Y. Miura, C. D. Manning, and C. P. Langlotz.  Contrastive learning of medical visual representations from paired images and text, 2020.
  * Zheng et al. [2017] L. Zheng, Y. Yang, and Q. Tian.  Sift meets cnn: A decade survey of instance retrieval, 2017.


# Temperature dependence of mobility of conducting polymer polyaniline with
secondary dopant

K. Yamada<EMAIL_ADDRESS>B. Shinozaki  T. Narikiyo  Y. Takigawa
Department of Physics, Kyushu University, Fukuoka, Japan  N. Kuroda  T. Bandou
H. Nakamura  Advanced Technology Research Laboratory, Idemitu Kosan Co. Ltd.,
Sodegaura, Japan

###### Abstract

The conductivity $\sigma$ and carrier density $n$ of the conducting polymer
polyaniline were investigated by changing the concentration $x$ of a secondary
dopant, meta-cresol. We found that $\sigma$ changes by four orders of
magnitude within the $x$-range of 1–10%, while $n$, as estimated from the Hall
measurements, shows a weak dependence on $x$ in the region of 2 % $<x<50$ %.
These results suggest that $\sigma$ can be enhanced by the change in the
mobility $\mu$. We analyzed the temperature dependence of $\mu$ by not only
the combination of two different types of scattering mechanism, but also by
the polaron hopping model. The experimental data of $\mu(T)$ can be explained
well by the latter model with reasonable fitting parameter values of a small-
polaron binding energy and a longitudinal optical phonon frequency.

###### keywords:

conducting polymer, polyaniline, mobility, Hall effect, polaron, hopping,
scattering

††journal: Journal of LaTeX Templates

##  1 Introduction

Conducting polymers can be solution-processed and are useful for low-cost
solar cells and printed circuits[1]. To improve devices for applications and
to understand the conduction mechanism, investigations of the mobility $\mu$
and carrier density $n$ of conducting polymers are very important. Although
there has been research on the mobility of the organic surface region in
contact with the insulator by the Hall effect and field effect for organic
field-effect transistors, the temperature dependence of the Hall mobility of
uniform conducting polymers has not been researched in-depth[2, 3, 4, 5, 6].
For simple conducting-polymer monolayer films, the temperature dependence of
$\mu$ and $n$ has not been independently reported, although the electrical
conductivity $\sigma$ has been extensively investigated from the viewpoint of
the metal-insulator transition[7].

Among various conductive polymers, polyaniline (PANI) is well-investigated[1].
The metallic transport properties of PANI have also been reported[8]. Doping
first with a substance such as a sulfosuccinic ether acid increases the hole
carrier concentration and enables PANI to dissolve in a solvent[1, 9, 10].
Furthermore, in terms of adaptation for a secondary dopant, it is known that
the conductivity of PANI is increased up to $\sim$10000 times than without a
secondary dopant[1, 11, 12]. MacDiarmid and Epstein reported that the effects
of secondary doping are based primarily on a change in molecular conformation
of PANI from a compact coil to an expanded coil that occurs during the
secondary doping process[12, 11]. Contrarily, optical studies of PANI have
been reported [1, 13, 14]. These optical studies suggest that the carriers are
polarons with a heavy effective mass. However, Lee et al.  reported that the
optical conductivity of high-conductivity PANI camphor sulfonic acid can be
successfully described by the simple Drude model without incorporating
contributions from the disorder-induced localization theory[1, 8]. To date,
however, systematic investigations of $\mu(T)$ from the viewpoint of
scattering mechanisms have not been extensively undertaken. We study the
origin of the significant enhancement of the conductivity caused by the
secondary dopant, meta-cresol(MCR), by measuring the dependences of $\sigma$
and $n$ on the dopant concentration. Further, we discuss in detail the
scattering mechanism of carriers of typical films in the crossover region
between high and low conductivities for a PANI film prepared with a controlled
MCR concentration.

##  2 Sample preparation and experimental procedure

To prepare the PANI films, we dissolved 3.6 g of the first dopant, dioctyl
sulfosuccinate sodium salt, and 3.74 g aniline in 100 mL toluene. Next, we
added 300 mL 1 N HCl to the mixture during cooling. Further, by adding a
mixture of 5.36 g ammonium persulfate (APS) and 100 mL 1 N HCl, the aniline
could polymerize, as the polymerization of PANI was carried out by chemical
oxidation using an APS oxidant in an aqueous solution. Dark green PANI
suspensions were obtained from this procedure. We removed the water and
volatile components from the above mixture to obtain the protonated PANI
complex solid. The solid PANI was dissolved using a mixture of toluene and the
secondary dopant, MCR, as the solvent, with a change in the ratio $x$(%) of
MCR to the PANI complex solid, where $x$ is defined by $x$=100 (mass of MCR) /
(mass of PANI complex solid). By casting the PANI melted in the solvents on a
polypropylene film with an area of 10 mm2, followed by drying for 18 h at 300
K and for 1 h at $\sim 350$ K in a grow box filled with N2 gas, we obtained
films with various resistivities, the film thickness for all specimens was
maintained at $15\mathrm{\mu m}$.

This measurement was performed by the four-terminal method with Hall bar
geometry. For the electrodes, we deposited thin Au contacts on the PANI films.
An external magnetic field $H$ was perpendicularly applied to the film
surface, of up to $H=1.35$ T. The equipment used for the Hall measurement was
reported in a previous paper[15]. We used the Keithley 6517B and 6514
electrometers for the DC voltage measurements, as well as the Keithley 220
programmable current source. After degassing at $T=313$ K in a vacuum for 1 h
to stabilize the resistance, we measured the temperature dependence of
$\sigma$ and $n$ in the temperature range of 80 K $<T<$ 300 K.

##  3 Experimental results and discussion

Figure 1:  Images of films (a) $x=0$% and (b) 10% obtained by scanning
electron microscopy.

Figure 2:  Schematics of conformations of polymers in Fig. 1. (a) bending
structure of polymers caused by attraction between ionized segments of the
polymer chain for the film without MCR and (b) extended structure polymer
chain for the film with MCR.

Fig. 1 shows the scanning electron microscope images for the films with (a)
$x$ = 0 and (b) $x$ = 10%. A considerable difference can be seen in the
conformation between the two films. Fig. 2 schematically shows the structures
of the films (a) without MCR and (b) with MCR. For film (a), prepared from
only the nonpolar solvent toluene without MCR, it is expected that the
conformation of polymers in the film take bending and/or bundle-like
structures, because the additional negative ions of the first dopant, between
the positively charged sites on the polymer chain, tend to decrease the
repulsive interaction and improve the compact coils of the polymer[12, 11]. As
the ratio of the more-polar MCR in the solvent is increased, the interaction
between the doped polymer chain and solvent also increases[12, 11]. The
solvation of the ions increased, resulting in their spreading further apart
and causing an expansion of the initial compact coil conformation of the PANI
chain, as shown in (b). Then, the conformation of the films with MCR seems to
be homogeneous compared with that of the films without MCR, that is, $x=0$. It
has been reported that MCR doping increases the crystallinity, given by the
sharp peaks observed in the X-ray diffraction spectrum of PANI with MCR[16].
Although carriers in the film with the extended polymers are delocalized, it
is expected that the carriers in a disordered bending polymer, that is, the
wavefunction, are localized by Anderson localization. This localization causes
low conductivity in disordered systems.

Figure 3:  The m-cresol concentration dependence of conductivity. The
$\sigma(T)$ for the films marked by the closed circle $(\bullet)$ is shown in
Fig. 8. The dashed line provides a guide for the eye.

The $x$-dependence of $\sigma$ at room temperature for PANI films over a wide
range of $x$ values is shown in Fig. 3. It was found that films with different
magnitudes of $\sigma$ showed the same value of $x$. This may be due to the
adding effect during different waiting times, from sample preparation to
measurement, and the uncontrollable conditions of film preparation. The aging
effect was expected to be dominant for low-$\sigma$ films when considering the
fact the instability of the conductivity is larger for less-conductive films.
Therefore, for films in an especially low $x$-region, $x<1$%, we considered
that higher values of $\sigma$ are reasonable, as shown by dotted line.

A large enhancement in $\sigma$ was observed in the region of $1\%<x<10\%$ as
$x$ increased. To find the reason for this strong dependence of $\sigma$ on
$x$, from the viewpoint of the scattering mechanism, it was necessary to first
investigate the $x$-dependence of $n$. We succeeded in measuring the value of
$n$ for films with $x\geq 2.5\%$ at room temperature. Particularly, for the
four films shown by closed marks, the $T$-dependence of $\sigma$, $n$, and the
mobility $\mu$ is shown in detail in Figs. 8, 9, and 11, respectively.

Figure 4:  Time evolution of the Hall voltage $V_{\mathrm{y}}$ of the films
with $x=10$% at $T=313$ K and $B=\pm 1$. The black dots and blue lines show
the experimental data and interpolation lines of Hall voltage, respectively.

As the resistance showed a gradual change with time, we measured the Hall
voltage $V_{\mathrm{y}}$ with a high accuracy over a sufficient time. In Fig.
4, typical data of the time-evolution of the $V_{\mathrm{y}}$ are shown for
the film $x=10$% at $T=313$ K and $B=\pm 1$ T with a period of 600 s,
indicated by the nearly rectangular function (right vertical axis). The black
and blue lines show the experimental data and expected values of
$V_{\mathrm{y}}$, respectively; the latter values were obtained by
interpolating the experimental data of $V_{\mathrm{y}}$ between the before and
after intervals. We determined the voltage difference $\Delta
V_{\mathrm{y}}=V_{\mathrm{y}}(B)-V_{\mathrm{y}}(-B)$ between the experimental
data and interpolation values.

Figure 5:  The magnetic field dependence of $\Delta
V_{\mathrm{y}}=V_{\mathrm{y}}(B)-V_{\mathrm{y}}(0)$ for the film $x=10$ % at
$T$ = 303 K and 86 K.

To clarify the linear relationship between $V_{\mathrm{y}}$ and $B$, data for
two typical temperatures are shown in Fig. 5, where the $\Delta
V_{\mathrm{y}}=V_{\mathrm{y}}(B)-V_{\mathrm{y}}(0)$ measurements were taken
between the two values $B=0$ and $\pm B$. As the magnetic field $B$ was
reversed, the voltage $\Delta V_{\mathrm{y}}$ also reversed. An accurate
linear relationship between $\Delta V_{\mathrm{y}}$ and $B$ was obtained (The
coefficient of determination $R^{2}=0.9998$ of the least squares method was
obtained for $x=10$ % at $T$ = 303 K). The linear relationship confirms the
high accuracy of the experimental data. Assuming the free electron model, the
carrier density $n$ can be obtained from the relationship:
$R_{\mathrm{H}}=E_{\mathrm{y}}/(B_{\mathrm{z}}j_{\mathrm{x}})=-1/(ne)$, where
$R_{\mathrm{H}}$, $E_{\mathrm{y}},j_{\mathrm{x}}$, and $B_{\mathrm{z}}$ are
the Hall coefficient, electrical field in the y-axis direction, current
density in the x-axis direction, and magnetic field in the z-axis direction,
respectively.

Figure 6:  The m-cresol concentration-dependence of carrier density at room
temperature. The temperature dependence of the films shown in the closed mark
are shown in Fig. 9. The dashed line provides a guide for the eyes.

At room temperature, the $x$-dependence of $n$ is shown in Fig. 6. The Hall
measurement was limited to a narrow region of $x$, compared with that of the
$\sigma$ measurement, due to a greater difficulty in accurate measurements of
$\Delta V_{\mathrm{y}}$ in films of a higher resistance ($x\leq 1$ (%)). At
room temperature, the standard errors of mean (SEM) of the films $x$= 2.5,
3.5, 5(%) were 7, 1.4, 0.6(%) of the measured value of $n$, respectively. The
reason for the data scattering is not due to the low accuracy of the Hall
voltage measurement, as shown in Fig. 5, but may be due to the uncontrollable
properties of the films, as mentioned above. Although the value of $n$ shows a
weak $x$-dependence with some scattering, it seems that $n$ is approximately
constant in the order of $\sim 10^{27}$/m3. This value indicates that the
carriers from the first dopant were fully excited at room temperature at any
$x$ concentration.

Figure 7:  The m-cresol concentration $x$-dependence of the mobility $\mu$ at
room temperature. As $x$ increases, $\mu$ increases. The temperature
dependence of the films shown by the closed marks is shown in Fig. 11. The
dashed line provides a guide for the eyes.

For $x<10\%$, as shown in Fig. 7, the value of $\mu$ estimated from the
relation $\mu=\sigma/(en)$ shows a similar $x$-dependence as that of $\sigma$.
Considering the weak $x$-dependence of $n$, we may conclude that the
$x$-dependence of $\sigma$ was mainly caused by the change in the mobility.

Figure 8:  The temperature dependence of the conductivity for the four typical films with different values of $x$: (a)3.5%, (b)5%, (c)10%, and (d)20%. Table 1:  Quantities obtained using $m^{\ast}$, acquired in the last section at room temperature. x(%) | $\rho(\Omega\cdot\mathrm{m})$ | $n(m^{-3})$ | $\epsilon_{F}(eV)$ | $\ell(\mathrm{m})$ | $k_{F}\ell$ | $d\rho/dT(\Omega\cdot\mathrm{m/K})$
---|---|---|---|---|---|---
3.5 | $2.2\times 10^{-3}$ | $1.9\times 10^{27}$ | 0.46 | $3.8\times 10^{-12}$ | 0.014 | $-2.1\times 10^{-6}$
5 | $6.8\times 10^{-4}$ | $4.2\times 10^{27}$ | 0.83 | $7.2\times 10^{-12}$ | 0.036 | $5.1\times 10^{-7}$
10 | $6.8\times 10^{-5}$ | $8.4\times 10^{27}$ | 1.44 | $4.6\times 10^{-11}$ | 0.29 | $4.3\times 10^{-3}$
20 | $2.5\times 10^{-4}$ | $3.1\times 10^{27}$ | 0.74 | $2.3\times 10^{-11}$ | 0.11 | $1.1\times 10^{-7}$

Fig. 8 (a) shows $\sigma(T)$ for the four films with different values of $x$,
as denoted by the closed mark in Fig. 3. The $\sigma(T)$ for all films shows
the insulating characteristic $d\sigma/dT>0$ in the low temperature region,
although the films with $x$ = 5% and 10% show metallic characteristics
$d\sigma/dT<0$ at temperatures of $T>250$ K, as shown in Figs. 8 (b) and (c).
We will analyze these four films in detail. Before discussions on the
$\sigma(T)$ characteristics, we will refer to the transport properties
estimated from the free electron model: $\mu=e\tau/m^{\ast}$,
$\ell=v_{\mathrm{F}}\tau$, $v_{\mathrm{F}}=\hbar k_{\mathrm{F}}/m^{\ast}$, and
$k_{\mathrm{F}}=(3\pi^{2}n)^{1/3}$, where $v_{\mathrm{F}}$ and
$k_{\mathrm{F}}$ are the Fermi velocity and the Fermi wavenumber,
respectively. Assuming the effective mass $m^{\ast}$ as that discussed in the
below Eq. (5), mean free path $\ell$, and Fermi energy $\epsilon_{F}$
calculated at room temperature are listed in Table 1. Even the longest
$\ell\sim$ 0.046 nm of the film with $x=10$% was shorter than the nearest
distance of 0.14 nm between the carbon atoms. When considering the Ioffe-Regel
criterion $k_{\mathrm{F}}\ell\sim 1$ for the metal-insulator (M-I) transition
and the experimental fact that the quantities $k_{\mathrm{F}}\ell$ for the
four films were in the range of $0.01<k_{\mathrm{F}}\ell<0.3$, the four films
seemed to be in an insulating region. These results indicate that the
transport properties of the preset films are no longer understood by the free
electron model and the mobility may be influenced by the Anderson-localization
effect. However, the discussion on the M-I criterion has not settled, and the
criterion values are not focused[17]. When considering the complex structures
of the presented polymer systems, it was necessary to examine the exact
structures and transport properties at sufficiently low temperatures for a
detailed discussion on the M-I transition.

Figure 9:  The temperature dependences of the carrier density in films with
m-cresol concentration (a) 3.5%, (b) 5%, (c) 10%, and (d) 20%. The error bars
in (a) and (b) show the standard error of the mean (SEM). The SEM of (c) and
(d) is similar to that of (b). The closed triangles show the data which were
measured one week after that of the open triangles. The dotted lines were
calculated from Eq. (1) to fit the experimental data. Figure 10:  Schematics
of the density of states, assumed by referring to three-dimensional amorphous
inorganic materials.

The condition $\epsilon_{\mathrm{F}}\gg k_{\mathrm{B}}T$ based on the free
electron model indicates the carrier fully degenerates and the carrier density
is constant with temperature. However, the experimentally-obtained carrier
density $n$ strongly depends on $T$, as shown in Fig. 9. Therefore, we assume
the following Eq. (1):

$n\propto\exp\left(-\frac{\epsilon_{n}}{k_{B}T}\right).$ (1)

After fitting Eq. (1) to the experimental data, we obtained the carrier
activation energy $\epsilon_{n}$ = 1.7, 3.5, 6.9, and 5.0 (meV) for the films
with $x$ =3.5(%), 5(%), 10(%), and 20(%), respectively. We obtained low-
precision data of the temperature-dependence of $n$ of the sample with 3.5%
and could not obtain data of a sample below 3.5%. Referring to the three-
dimensional (3D) amorphous inorganic materials, we assumed the density of
states of PANI, as shown in Fig 10. The bandgap of PANI
($\epsilon_{\mathrm{g}}=E_{\mathrm{C}}-E_{\mathrm{V}}$) was obtained
experimentally in[13] ($\epsilon_{\mathrm{g}}\sim$1.5 eV) and theoretically
in[18] ($\epsilon_{\mathrm{g}}\sim$1.3 eV), the values of which are larger
than the $\epsilon_{n}$ obtained for the films used in this study. This
indicates that the simple band-conduction model cannot yet be applied but the
localized states due to the Anderson localization effect are required in such
dirty systems as the presented polymers.

A mobility edge is defined as the energy separating the localized and
nonlocalized states in the conduction or valence bands of a 3D noncrystalline
material. The hatched area by the vertical lines in Fig. 10 shows the
localized discontinuous states. The blue area shows the electrons fully
occupying the states. Unge and Christen determined the electron and hole
mobility edges in amorphous polyethylene by calculating the boundary between
the localized and delocalized states in energy-space[19]. When it is assumed
that the electron excites with the activation energy
$\epsilon_{\mathrm{n}}=E_{\mathrm{F}}-E_{\mu}$ and the generated hole under
the hole mobility edge $E_{\mu}$ can move, the relation $n\propto
e^{-\epsilon_{n}/k_{B}T}$ is expected. As $x$ increased, and the disorder
decreased, it was predicted that $E_{\mu}$ increases, to result in the
decreasing of $\epsilon_{\mathrm{n}}$ and increasing of $n$. However, the
experimental results show that $n$ increased but $\epsilon_{n}$ also increased
with increasing $x$. This discrepancy suggests that the mobility edge cannot
be sharply defined in the conducting polymer PANI. For a distinct discussion,
the Hall measurement is needed in the lower temperature region. There is a
polaron mechanism for lowering mobility and localizing electrons. The carrier
of the conducting polymers is a polaron-soliton, which has a solitary wave.
The localization length can be much larger than the soliton size[20]. A
polaron-soliton can be localized by Anderson localization.

Figure 11:  The temperature dependence of the Hall mobility for m-cresol
concentration (a) 3.5%, (b) 5%, (c) 10%, and (d) 20%. The black dash and red
sold lines were calculated from Eqs. (4) and (5) to fit the experimental data,
respectively.

Figs 11 show the $T$-dependence of $\mu$ for the four films shown in Fig. 8
and Fig. 9. Although $\mu(T)$ for the films with $x=10$% and 3.5% show a
monotonic change, the $\mu(T)$ for the films with $x=5$% show a maximum at
around $T=250$ K. Such $T$-dependence, showing the transition between a
positive and negative temperature coefficient of resistivity, has been
reported for PANI blends [7] with $\sigma\sim 10^{4}~{}\mathrm{S/m}$, although
high-conductivity PANI films with $\sigma\sim 10^{5}~{}\mathrm{S/m}$ can be
successfully described by the simple Drude model without incorporating
contributions from the disorder-induced localization theory[8]. For PANI-CSA
and PANI-DBSA composite films, with the low conductivity mentioned above, the
authors [7] analyzed $\rho(T)$ by the sum of the mechanism of quasi-1D
metallic conduction in the ordered regions, and the 3D variable-range hopping
conduction in the disordered region. Considering $\sigma(T)$ with
$\sigma<10^{4}\mathrm{S/m}$ at room temperature, the contributions from the
disorder-induced localization cannot be neglected.

In order to reproduce $\mu(T)$ for the present PANI films by the combination
of opposite characteristics, we show some scattering mechanisms. In ordered
metallic polymers, the $\mu_{\mathrm{ph}}$ due to back-scattering thermal
phonons is given by[1]:

$\mu_{\mathrm{ph}}=\frac{ea^{2}m\omega_{0}t^{2}_{0}}{4\pi\alpha_{1}^{2}\hbar^{2}}\exp\left(\frac{\hbar\omega_{0}}{k_{B}T}\right)$
(2)

where $\alpha_{1}$ (eV/Å) describes the magnitude of electron-phonon
interaction, $\omega_{0}$ is the phonon frequency, $t_{0}$ is the transfer
interaction (2.7 eV), and $a$ is the carbon-carbon spacing (0.14 nm). In
semiconducting crystals, ion-dopant atoms cause ionized impurity
scattering[21]. Brooks and Herring calculated the ionized impurity scattering
time as $\tau_{\mathrm{ion}}\sim T^{3/2}$. Using a characteristic temperature
$T_{1}$ and the characteristic mobility ($\mu^{\ast}=2.2\times
10^{-5}~{}(\mathrm{m}^{2}/\mathrm{Vs})$), we assume the following equation:

$\mu_{\mathrm{ion}}=\mu^{\ast}(T_{1}/T)^{-3/2}$ (3)

Assuming that the total relaxation rate $1/\tau$ is expressed by the
relationship: $1/\tau=1/\tau_{\mathrm{ph}}+1/\tau_{\mathrm{ion}}$, we
attempted to fit the following expression:

$1/\mu=1/\mu_{\mathrm{ph}}+1/\mu_{\mathrm{ion}}$ (4)

to the experimental data of the mobility. Using the fitting parameters
$T_{1},\omega_{0}$ and $\alpha_{1}$ in Eqs. (2) and (3), the black dashed
lines in Fig. 11 were calculated. We used the fitting parameters
$T_{1}=250,140,20,53$ (K), $\alpha_{1}=0.135,0.125,0.235,0.227$, and
$\hbar\omega_{\mathrm{0}}=0.017,0.030,0.017,0.024$(meV) for the films with
$x=3.5,5,10,20$ (%), respectively.

Figure 12:  The m-cresol concentration-dependence of (a) the hopping energy $W_{\mathrm{H}}$ and (b) the phonon energy $\hbar\omega_{\mathrm{LO}}$, obtained by fitting Eq. (5) to the mobility $\mu(T)$ data, and (c) the electron-phonon coupling constant $\alpha$.  $x$(%) |  $\epsilon_{\mathrm{n}}$(meV) |  $W_{\mathrm{H}}$(meV) |  $\hbar\omega_{\mathrm{LO}}$(meV)
---|---|---|---
3.5 | 1.7 | 30 | 26
5 | 3.5 | 19.5 | 25
10 | 6.9 | 8.5 | 76
20 | 5.0 | 10 | 67
Table 2: The activation energy of carriers $\epsilon_{\mathrm{n}}$ obtained by
fitting Eq. (1) to the $T$ dependence of the carrier density. The values
$W_{\mathrm{H}}$ and $\hbar\omega_{\mathrm{LO}}$ were obtained by fitting Eq.
(5) to the $T$ dependence of the mobility.

In contrast, the theory for the small polaron mobility [22, 23, 24] results in
the following formula:

$\mu_{\mathrm{sp}}=\frac{ea^{2}\omega_{\mathrm{LO}}}{6k_{\mathrm{B}}T}\exp\left(-\frac{W_{\mathrm{H}}}{k_{\mathrm{B}}T}\right).$
(5)

where $a$ is the lattice constant of the crystal in which the small polaron
occurs, $W_{\mathrm{H}}$ is the thermal activation energy for hopping and is
given by half the small-polaron binding energy $E_{\mathrm{b}}$, and
$\omega_{\mathrm{LO}}$ is the frequency of the longitudinal optical phonon.
For $a$, we adopted the distance of carbon-carbon atoms as 0.14 nm. We fitted
Eq. (5) to the data of $\mu(T)$ using the fitting parameters
$\omega_{\mathrm{LO}}$ and $W_{\mathrm{H}}$, as shown by the red lines in Fig.
11. The $x$-dependence of $W_{\mathrm{H}}$ and $\hbar\omega_{\mathrm{LO}}$
shown in Fig. 12 (a) and (b) are reasonable, when it is taken into account
that the increase in $x$ results in an increase of crystallinity. These
results suggest that the polymer becomes harder and the lattice deformation
due to the polaron becomes weaker with the increase in $x$ ($x<10$). From the
data of thermal conductivity, Nath et al. [25] estimated $\Theta_{\mathrm{D}}$
of PANI nanofibers without a secondary dopant to be approximately 240-300 K,
which corresponds to $\hbar\omega_{\mathrm{LO}}$ = 21–26 meV under the
assumption $\hbar\omega_{\mathrm{LO}}=k_{\mathrm{B}}\Theta_{\mathrm{D}}$. For
metallic polyacetylenes with high conductivity $\sigma\sim 10^{7}$ (S/m),
$\hbar\omega_{0}$ is 0.12 eV (1400 K) [1]. These facts are consistent with the
presented experimental result that $\hbar\omega_{\mathrm{LO}}$ increases with
the increase in $\sigma$, that is, $x$. Contrarily, MacDarmid and Epstein
reported the absorption spectrum of PANI with various secondary dopants[12].
The absorption peak of a localized polaron was observed in the spectrum of
PANI ($\sigma\sim 10^{-3}\mathrm{S/m}$) but the peak diminished in that of
PANI ($\sigma\sim 1.2\times 10^{4}\mathrm{S/m}$). This corresponds to the
decrease in $W_{\mathrm{H}}$ with increasing $\sigma$, that is, $x$ in Fig.
12(a).

Strictly speaking, Eq.(5) is valid under the condition
$T>\Theta_{\mathrm{D}}/2$. At the low temperature region, the contribution of
quantum tunneling cannot be neglected[24]. Then, it can be predicted that the
mobility is larger than that estimated from Eq.(5)[26]. This contribution may
be the reason for the difference between the experimental data and the theory
from Eq. (5) in Fig. 11.

Feynman calculated the ground state energy $E_{0}$ of a polaron with the
energy of an uncoupled electron-phonon system as zero energy and the mass
$m^{\ast}$ of polaron as follows[27]:
$E_{0}/(\hbar\omega_{\mathrm{LO}})=-\alpha-0.0123\alpha^{2}-0.00064\alpha^{3}\cdots$
and $m^{\ast}/m_{e}=1+\alpha/6+0.025\alpha^{2}+\cdots$, where $\alpha$ is the
electron-phonon coupling constant. Assuming that $E_{0}$ is equal to the
polaron binding energy $-E_{b}=-2W_{\mathrm{H}}$, we obtained an
$x$-dependence of $\alpha$, as shown in Fig. 12(c), then the effective mass
ratio $m^{\ast}/m_{\mathrm{e}}=$1.48, 1.31, 1.04, 1.05 in the films with
$x$=3.5, 5, 10, and 20, respectively. Using the value of $m^{\ast}$, we
estimated the value of $\tau$, $E_{\mathrm{F}}$, and $T_{\mathrm{F}}$, given
in Tables 1 and 2. The increase in $x$ results in the decrease in the
electron-phonon coupling strength. This result suggests that weakening of the
electron-phonon coupling is needed for the enhancement of $\sigma$ of organic
materials.

The polaron model fitted the data better than the band scattering model. The
values of the parameters obtained by the fitting are reasonable. The
Ioffe–Regel criterion $k_{F}\ell<1$ suggests that the hopping model is better
than the band model. Thus, we conclude the polaron hopping model is suitable.

##  4 Conclusions

We measured the Hall effect of conducting polymer PANI films to obtain
separately the mobility $\mu$ and the carrier density $n$ for PANI films with
various concentrations $x$ of MCR. From these results, we found that the
enhancement in $\sigma$ is mainly as a result of the change in the mobility
$\mu$. We also measured the temperature-dependence of $n$ and $\mu$. With a
decrease in $T$, $n$ decreases. We discussed the $x$-dependence of the
activation energy of the carrier and concluded that a mobility edge cannot be
clearly defined. We analyzed the $\mu(T)$ for four typical films with
different values of $x$ using two scenarios: the combination of scattering
models with opposite characteristics of $\mu(T)$ and the small-polaron hopping
model. The polaron model fitted the data better than the band scattering
model. The parameters obtained by the fitting of the polaron model were
reasonable. With an increase in $x$, $W_{\mathrm{H}}$ and the electron-phonon
coupling constant $\alpha$ decrease but the phonon energy
$\omega_{\mathrm{LO}}$ increases. It is considered that these dependences
cause enhancement by the crystallinity. Finally, the presented analysis
suggests that the weakening of electron-phonon coupling is necessary to
enhance the conductivity of organic materials.

##  5 Acknowledgement

The experiment was performed at the cryogenic center of Kyushu University. The
authors thank Mr. Y. Ueda for the supply of liquid nitrogen. The authors thank
Prof. N. Kuramoto for the preparation method of PANI. We thank Dr. K. Makise,
Dr. N. Kokubo, and Dr. T. Asano for various contributions. English
proofreading and publication fee were supported by JSPS KAKENHI Grant Number
JP17K06303 and JP16K04877.

## References

## References

  * [1] A. Heeger, N. S. Sariciftci, E. B. Namdas, Semiconducting and Metallic Polymers, Oxford university Press, 2010.
  * [2] M. Yamagishi, J. Soeda, T. Uemura, Y. Okada, Y. Takatsuki, T. Nishikawa, Y. Nakazawa, I. Doi, K. Takimiya, J. Takeya, Phys. Rev. B 81 (2010) 161306(R).  doi:10.1103/PhysRevB.81.161306.
  * [3] T. Uemura, M. Yamagishi, J. Soeda, Y. Takatsuki, Y. Okada, Y. Nakazawa, J. Takeya, Temperature dependence of the hall effect in pentacene field-effect transistors: Possibility of charge decoherence induced by molecular fluctuations, Phys. Rev. B 85 (2012) 035313.  doi:10.1103/PhysRevB.85.035313.
  * [4] X. Yu, J. Yu, J. Zhou, J. Huang, Y. Jiang, Appl. Phys. Lett. 99 (2011) 063306.  doi:10.1063/1.3624586.
  * [5] B. Lee, Y. Chen, D. Fu, H. T. Yi, K. Czelen, H. Najafov, V. Podzorov, Trap healing and ultralow-noise hall effect at the surface of organic semiconductors, Nature Mater. 12 (2013) 1125–1129.  doi:10.1038/nmat3781.
  * [6] S. P. Senanayak, A. Z. Ashar, S. P. Catherine Kanimozhi, K. S. Narayan, Room-temperature bandlike transport and hall effect in a high-mobility ambipolar polymer, Phys. Rev. B 91 (2015) 115302.  doi:10.1103/PhysRevB.91.115302.
  * [7] Y. Long, Z. Chen, N. Wang, J. Li, M. Wan, Electronic transport in PANI-CSA/PANI-DBSA polyblends, Physica B 344 (2004) 82–87.  doi:10.1016/j.physb.2003.09.245.
  * [8] K. Lee, S. Cho, S. H. Park, A. J. Heeger, C.-W. Lee, S.-H. Lee, Metallic transport in polyaniline, Nature 441 (2006) 65–68.  doi:10.1038/nature04705.
  * [9] N. Kuramoto, A. Tomita, Aqueous polyaniline suspensions: Chemical oxidative polymerization of dodecylbenzene-sulfonic acid aniline salt, Polymer 38 (1997) 3055–3058.  doi:10.1016/S0032-3861(96)00861-0.
  * [10] S.-J. Su, N. Kuramoto, Synthesis of processable polyaniline complexed with anionic surfactant and its conducting blends in aqueous and organic system, Synth. Met. 108 (2000) 121–126.  doi:10.1016/S0379-6779(99)00185-X.
  * [11] A. G. MacDiarmid, A. J. Epstein, Secondary doping in polyaniline, Synth. Met. 69 (1995) 85–92.  doi:10.1016/0379-6779(94)02374-8.
  * [12] A. G. MacDiarmid, A. J. Epstein, The concept of secondary doping as applied to polyaniline, Synth. Met. 65 (1994) 103–116.  doi:10.1016/0379-6779(94)90171-6.
  * [13] S. Stafström, J. L. Bredas, A. J. Epstein, H. S. Woo, D. B. Tanner, W. S. Huang, A. G. MacDiarmid, Polaron lattice in highly conducting polyaniline: Theoretical and optical studies, Phys. Rev. Lett. 59 (13) (1987) 1464–1467.  doi:10.1103/PhysRevLett.59.1464.
  * [14] R. S. Kohlman, J. Joo, Y. G. Min, A. G. MacDiarmid, A. J. Epstein, Phys. Rev. Lett. 77 (3) (1996) 2766–2769.  doi:10.1016/S0379-6779(96)04115-X.
  * [15] K. Yamada, B. Shinozaki, K. Yano, H. Nakamura, J. Phys. Conf. Ser. 400 (2012) 042069\.  doi:10.1088/1742-6596/400/4/042069.
  * [16] S. J. Varm, F. Xavier, S. Varghese, S. Jayalekshmi, Synthesis and studies on exceptionally crystalline polyaniline thin films, Polym Int 61 (2012) 743–748.  doi:10.1002/pi.4131.
  * [17] K. Makise, B. Shinozaki, T. Asano, K. Mitsuishi, K. Yano, K. Inoue, H. Nakamura, Relationship between variable range hopping transport and carrier density of amorphous In2O3-10wt % ZnO thin films, J. Appl. Phys. 112 (2012) 033716.  doi:10.1063/1.4745055.
  * [18] O. Kwon, M. L. McKee, Calculations of band gaps in polyaniline from theoretical studies of oligomers, J. Phys. Chem. B 104 (2000) 1686–1694.  doi:10.1021/jp9910946.
  * [19] M. Unge, T. Christen, Electron and hole mobility edges in polyethylene from materialsimulations, Chem. Phys. Lett. 613 (2014) 15–18.  doi:10.1016/j.cplett.2014.08.058.
  * [20] K. Sacha, C. A. Müller, D. Delande, J. Zakrzewski, Phys. Rev. Lett. 103 (2009) 210402.  doi:10.1103/PhysRevLett.103.210402.
  * [21] K. Seeger, Semiconductor Physics, Springer-Verlag, 2004.
  * [22] V. L. Gurevich, I. G. Lang, Y. A. Firsov, Sov. Phys. Solid State 4 (1963) 918–.
  * [23] J. T. Devreese, Polarons, Encyclopedia of Applied Physics 14 (1996) 383–409.  arXiv:cond-mat/0004497v2.
  * [24] S. N. Mott, Conduction in Non-Crystalline Materials, Oxford university Press, 1987\.
  * [25] C. Nath, A. Kumar, K. Z. Syu, Y. K. Kuo, Heat conduction in conducting polyaniline nanofibers, Appl. Phys. Lett. 103 (2013) 121905.  doi:10.1063/1.4821656.
  * [26] T. Holstein, Studies of polaron motion: Part ii. the small polaron, Ann. Phys. 8 (1959) 343–389.  doi:10.1016/0003-4916(59)90003-X.
  * [27] R. P. Feynman, Slow electrons in a polar crystal, Phys. Rev. 97 (1955) 660–665.  doi:10.1103/PhysRev.97.660.