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Compare the following two sentences, "ため" is used to express 原因 in both
sentences:

> 寒さの **ために** 死んだ。
>
> 日本は島国の **ため** 、陸上には国境がない。

I wonder if I can choose to add the particle "に" as I want,

but one of my Japanese friend told me

> 寒さの **ため** 死んだ。（✕）
>
> 日本は島国の **ために** 、陸上には国境がない。（✕）

don't sound natural.

Does anyone know the rule when we should add "に" or not?
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question
particles particle-に
When is the particle "に" redundant in the phrase "ために"
> 寒さ **のために** 死んだ。

The のために means "due to~" " _all_ because of~" " _only/primarily_ for the
reason of~".  
～ために has a nuance of "the result was caused **only/primarily** for this
reason", and its main clause, or apodosis, (「死んだ」 here) should usually be an
**unfavorable/unwelcomed result**.  
The sentence can be rephrased as: 寒さ **のせいで** 死んだ。  
「～のせいで～」「～のために～」 could have a blaming or regretting tone.  
(I think 「寒さのため死んだ。」 is also acceptable.)

Whereas...

> 日本は島国の **ため** 、陸上には国境がない。

The ため means "because~" "~so" or "therefore".  
日本は島国のため **に** 、陸上には国境がない wound sound a little unnatural because 陸上に国境がない is
not really an _unfavorable_ result.  
It can be rephrased as: 日本は島国な **ので** /だ **から** 、～～。  
When using 「～のため、～」「～なので・だから、～」, the connection of the "reason/cause" and the
"result" tends to sound weaker than 「～のために」「～のせいで」.

* * *

Similar examples...

  * 「道が狭い **ために** 、車が入れない。」(≂道が狭い **せいで** ～) (Example taken from 明鏡国語辞典)  
My car can't go through due to the fact that the street is narrow. -- the
_unfavorable_ result is caused _all because_ / _only for the reason_ that the
street is narrow.  
(I think 「道が狭いため、車が入れない」 is also acceptable.)

  * 「道が狭い **ため** / [狭路]{きょうろ}の **ため** 、[迂回]{うかい}してください。」(≂道が狭い **ので** ～ / 狭路 **なので** ～)  
The street is narrow, so please take a detour.  
(×「道が狭いため **に** /狭路のため **に** 、迂回してください。」 doesn't sound right.)

Also compare:

  * 「無理をしたため **に** 病気になった」 I got sick _all because_ I pushed myself too much. 
  * 「美しさのため **に** 人から妬まれる」 Others are jealous of me _only for/all because of_ my beauty.  
and...

  * 「家が手狭なため、改築する」 Our house is small, so we'll rebuilt it.  
(Examples taken from 明鏡国語辞典)
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answer
"に" is used to emphasise the reasons in these sentences. All expressions
you've picked up are linguistically right, but the problem they two sound
unnatural is here and it depends on what the speaker really want to tell us.
<http://blog.livedoor.jp/s_izuha/archives/2427356.html>

> 寒さのために死んだ。
>
> 日本は島国のために、陸上には国境がない。

It makes us focus on the reasons.

> 寒さのため死んだ。
>
> 日本は島国のため、陸上には国境がない。

It makes us focus on the facts.

Instance translation:

```

    寒さのために死んだ。 → It is because it was too cold, the person died.
    
    寒さのため死んだ。 → The person did die because it was too cold.
    
```

And I also feel not only "日本は島国のために" but "日本は島国のため" to be odd. "寒さ" is a
outside cause and the noun could be the reason, but "島国" is not the cause. No
island can erase Japanese border on land. Of course, "being island" is the
cause. I mean "日本は島国のため" is not enough and, strictly, it should be "日本は島国
**である** ため." Both of "日本は島国のために" and "日本は島国のため" aren't precisely right,
althogh we Japanese often use it.

The reason why your friend said it sounded wrong is the emphasis effect of
"に".

> 日本は島国のために、陸上には国境がない。

As I said, "に" in this sentence emphasises the reason. To be precise, I meant
it was the reason which was a noun. So this "に" emphasises only "島国" even
though the actual reason is not "island" but "being island." I think it makes
itself a little odd.
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answer
The existing answers here focus on native speakers' understanding of emphasis,
which are very useful.

I'd also like to propose a grammatical explanation for the use of に in ために.
From page 450 of _A Dictionary of Basic Japanese Grammar_ ,

> The _ni_ of _tame ni_ can be dropped, if a phrase intervenes between the
> main verb and _tame ni_.

For example,

> 日本人は会社のためによく働きます。(に is required, the verb is right after ために)
>
> 雪のため（に）学校が休みになった。(に is optional, 学校 is between ために and the verb)

There may indeed be a difference in nuance when the に is optional. Also,
[Geika's answer](https://japanese.stackexchange.com/a/56196/12216) states that
`寒さのため死んだ` is a valid sentence, which apparently is grammatically incorrect,
but may be a colloquial wording.
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